84.40.4 problem 27.9

Internal problem ID [22379]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 27. Solutions of systems of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 27.9
Date solved : Thursday, October 02, 2025 at 08:38:04 PM
CAS classification : system_of_ODEs

\begin{align*} w^{\prime }\left (t \right )-y&=0\\ w \left (t \right )+y^{\prime }+z \left (t \right )&=1\\ w \left (t \right )-y+z^{\prime }\left (t \right )&=2 \sin \left (t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ w \left (0\right )&=1 \\ z \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 2.645 (sec). Leaf size: 201210

ode:=[diff(w(t),t)-y(t) = 0, w(t)+diff(y(t),t)+z(t) = 1, w(t)-y(t)+diff(z(t),t) = 2*sin(t)]; 
ic:=[y(0) = 1, w(0) = 1, z(0) = 1]; 
dsolve([ode,op(ic)]);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 2659

ode={D[w[t],t]-y[t]==0,w[t]+D[y[t],t]+z[t]==1,w[t]-y[t]+D[z[t],t]==2*Sin[t]}; 
ic={y[0]==1,w[0]==1,z[0]==1}; 
DSolve[{ode,ic},{y[t],w[t],z[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
w = Function("w") 
z = Function("z") 
ode=[Eq(-y(t) + Derivative(w(t), t),0),Eq(w(t) + z(t) + Derivative(y(t), t) - 1,0),Eq(w(t) - y(t) - 2*sin(t) + Derivative(z(t), t),0)] 
ics = {y(0): 1, w(0): 1, z(0): 1} 
dsolve(ode,func=[y(t),w(t),z(t)],ics=ics)
 

OverflowError : mpz too large to convert to float